Algebra Examples

$3 x^{2} + 3 x - 90 = 0$

Step 1

Factor $3$ out of $3 x^{2} + 3 x - 90$ .

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Step 1.1

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) + 3 x - 90 = 0$

Step 1.2

Factor $3$ out of $3 x$ .

$3 (x^{2}) + 3 (x) - 90 = 0$

Step 1.3

Factor $3$ out of $- 90$ .

$3 (x^{2}) + 3 x + 3 \cdot - 30 = 0$

Step 1.4

Factor $3$ out of $3 (x^{2}) + 3 x$ .

$3 (x^{2} + x) + 3 \cdot - 30 = 0$

Step 1.5

Factor $3$ out of $3 (x^{2} + x) + 3 \cdot - 30$ .

$3 (x^{2} + x - 30) = 0$

Step 2

Factor.

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Step 2.1

Factor $x^{2} + x - 30$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 30$ and whose sum is $1$ .

$- 5, 6$

Step 2.1.2

Write the factored form using these integers.

$3 ((x - 5) (x + 6)) = 0$

Step 2.2

Remove unnecessary parentheses.

$3 (x - 5) (x + 6) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x + 6 = 0$

Step 4

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 4.2

Add $5$ to both sides of the equation.

$x = 5$

Step 5

Set $x + 6$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Step 5.2

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 6

The final solution is all the values that make $3 (x - 5) (x + 6) = 0$ true.

$x = 5, - 6$